E-values (wikipedia) are an alternative to p-values that effortlessly deal with optional continuation: with e-value based tests and the corresponding anytime valid (AV) confidence intervals, one can always gather additional data, while keeping statistically valid conclusions. Until 2019, publications on e-values were few and far between: the concept did not even have a name. Then, in the course of a few months, four papers by different research groups, (including ours – see below) appeared on arXiv that firmly established them as an important statistical concept. By now, there are 100s of papers on e-values and there have been two international workshops on the topic. Allowing for optional continuation is just one way in which e-values provide more flexibility than p-values – they also allow to set a type of significance/confidence level alpha after seeing the data, which is a mortal sin in classical testing. In this talk I will introduce e-values, e-processes and AV confidence intervals, and discuss how like Bayesian approaches, they employ priors, while, unlike in Bayesian approaches, we obtain error guarantees even if these priors misalign with the data.

Main literature:
G., De Heide, Koolen. Safe Testing. Journal of the Royal Statistical Society Series B, 2024 (first version appeared on arXiv 2019).
G. Beyond Neyman-Pearson: e-values enable hypothesis testing with a data-driven alpha. Proceedings National Academy of Sciences of the USA (PNAS), 2024.